Related papers: Approximating the XY model on a random graph with …
This thesis focuses on the XY model, the simplest vector spin model, used for describing numerous physical systems. It is studied for different sources of quenched disorder: random couplings, random fields, or both them. The belief…
We investigate an XY spin-glass model in which both spins and couplings evolve in time: the spins change rapidly according to Glauber-type rules, whereas the couplings evolve slowly with a dynamics involving spin correlations and Gaussian…
We investigate an XY spin-glass model in which both spins and interactions (or couplings) evolve in time, but with widely separated time-scales. For large times this model can be solved using replica theory, requiring two levels of…
We study a nearest neighbors ferromagnetic spin system on the square lattice in which the spin field is constrained to take values in a discretization of the unit circle consisting of $N$ equi-spaced vectors, also known as $N$-clock model.…
Large-scale simulations have been performed in the current-driven three-dimensional XY spin glass with resistively-shunted junction dynamics for sample sizes up to $64^3$. It is observed that the linear resistivity at low temperatures tends…
The $XY$ model with four-body quenched disordered interactions and its discrete $p$-clock proxy is studied on bipartite random graphs by means of the cavity method. The phase diagrams are determined from the ordered case to the spin-glass…
We study the effects of discretization on the U(1) symmetric XY model in two dimensions using the Higher Order Tensor Renormalization Group (HOTRG) approach. Regarding the $Z_N$ symmetric clock models as specific discretizations of the XY…
The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain…
We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by…
We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient…
We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an…
We study a large-$N$ bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the $p$-spin spherical model. Replica symmetry is broken at low temperatures and for…
We analyze the zero-temperature behavior of the XY Edwards-Anderson spin glass model on a square lattice. A newly developed algorithm combining exact ground-state computations for Ising variables embedded into the planar spins with a…
We revisit the long time dynamics of the spherical fully connected $p = 2$-spin glass model when the number of spins $N$ is large but {\it finite}. At $T=0$ where the system is in a (trivial) spin-glass phase, and on long time scale $t…
In this paper we prove the weak convergence, in a high-temperature phase, of the finite marginals of the Gibbs measure associated to a symmetric spherical spin glass model with correlated couplings towards an explicit asymptotic decoupled…
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
In this paper we study a fully connected planted spin glass named the planted XY model. Motivation for studying this system comes both from the spin glass field and the one of statistical inference where it models the angular…
Our goal in this work is to better understand the relationship between replica symmetry breaking, shattering, and metastability. To this end, we study the static and dynamic behaviour of spherical pure $p$-spin glasses above the replica…
For many real spin-glass materials, the Edwards-Anderson model with continuous-symmetry spins is more realistic than the rather better understood Ising variant. In principle, the nature of an occurring spin-glass phase in such systems might…
The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state…